For Exercises 45–50, write out the first three terms and the last...

Question

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

Summation formula for an arithmetic sequence from i=1 to 30 of (-3i + 5).

Accepted Answer

Hey everyone in this problem we are asked to identify the first four terms in the last term and to evaluate the some using the formula given S. N. Is equal to N over two. A One plus A. M. Now we're giving the summation i is equal to 1 to 34 of negative five I plus eight. Alright so let's start with the terms. So the first term We're starting with I is equal to one here on the bottom of estimation. So the first term corresponds to this I value we're going to get I. Is equal to one and our term is given by negative five. I plus eight. We're gonna get negative five times one plus eight Which is going to be three. Alright now for our second term. Okay so we're starting at I equals one and then I just increases by one each time. So for our second term we're gonna have eyes equal to two. We're gonna get negative five times I which is two plus eight. Okay so we have negative 10 plus eight. We get negative two. Following the same pattern. The third term is equal to three negative five times three plus eight. That's negative 15 plus eight negative seven. And the 4th term I is equal to four. Fourth term sorry is equal to four. Okay we get negative five times four plus eight. That's -40-plus 8 which is negative sorry negative 20 negative 20 plus eight minus 12. There we go. Okay. Always double check your work. So you don't make silly mistakes. All right now we need to do the last term. Okay, we found the first four terms. Now we need to do the last term. Now the last term is going to be given that the end value and this is gonna be the value up here. Okay? So we're gonna take I starting at one all the way up until I is 34. Okay, so the last term is going to happen when I is equal to 34. So what we're gonna get is we're gonna get negative five times plus eight. Which is going to be equal to -162. Alright, So we found the terms first four and the last now we're asked to evaluate the some Okay, So the sum formula S N is equal to n over two times a one plus A N. Now, A when we're talking about A is a term. Okay, So a one is the first term. A N. Is the 10th term. Okay. And is going to be the number of terms we have. Okay. Or when we're starting at one in our summation then it's just gonna be this top value 34 or the top Value that I will eventually go to. Okay, so in this case we have N is 34 divided by two. A one is the first term which we found is three and A N. Well, that's going to be the 34th term, which is the same as the last term. Okay. Which is negative 1 62. All right. And this is gonna give us a sum of -2703. Okay. All right. So looking at our possible answers, we have the first four terms are three negative two negative seven negative 12. The last term is negative 162 and the sum is negative 2703. This is gonna be answer. A thanks everyone for watching. I hope this video helped see you in the next one.

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

Key Concepts

Arithmetic Sequence

Summation Notation

Sum of an Arithmetic Sequence Formula

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